please, please, please tell me some good 2 player games - give away added

Nidhogg

You can also filter the store in sites like this, I believe the local co-op tag is what you want [In the same site you can search your own library]

Most of the LEGO games, like Harry Potter, Star Wars, or The Lord of the Rings. They are great for co-op, and have lots of replayability if you like collecting and unlocking content.

Unrailed is also very fun. I believe it supports 2 simultaneous players on one PC using only the keyboard (eg. one person uses the numpad).

Just use Steam's search.
This one offers all games with a rating of 85 or higher and shared/split screen: https://store.steampowered.com/search/?sort_by=Reviews_DESC&as-reviews-score=85-&category3=24
Add tags if you look for specific genres/tags. With Beat'em ups only: https://store.steampowered.com/search/?sort_by=Reviews_DESC&term=Beat%20%27Em%20Up&as-reviews-score=85-&category3=24

Mayhem Brawler
https://store.steampowered.com/app/1306720/Mayhem_Brawler/

You can filter for games with local co-op in the steam store: https://store.steampowered.com/search/?sort_by=Reviews_DESC&category1=998&category2=39
Or on steamdb: https://steamdb.info/instantsearch/?refinementList%5Btags%5D%5B0%5D=Local%20Co-Op&refinementList%5BappType%5D%5B0%5D=Game
My personal recommendation is: https://store.steampowered.com/app/238460/BattleBlock_Theater/

Advanture Pals

Kingdom Two Crowns (Management): https://store.steampowered.com/app/701160/Kingdom_Two_Crowns_Play_the_Norse_Lands_Demo/

Castle Crashers (Beat 'em up): https://store.steampowered.com/app/204360/Castle_Crashers/

Streets of Rage 4 (Beat' em up): https://store.steampowered.com/app/985890/Streets_of_Rage_4/

BattleBlock Theater (Puzzle): https://store.steampowered.com/app/238460/BattleBlock_Theater/

Tricky Towers (Puzzle): https://store.steampowered.com/app/437920/Tricky_Towers/

Crawl (Dungeon crawler): https://store.steampowered.com/app/293780/Crawl/

It takes two is getting some good reviews and is in sale.

Ibb & Obb: https://store.steampowered.com/app/95400/ibb__obb/
Fling to the Finish: https://store.steampowered.com/app/1054430/Fling_to_the_Finish/

BTW Fling to the Finish looks hilarious and reviews are good. I think you'd get a laugh out of it. I have it, but haven't had the chance to play it yet. There is a gameplay stream on the Steam store for it.

Huntdown has a 2-player mode and it's really good, but it's a bit on the challenging side.

Untitled Goose Game is chaotic, silly fun and it's a good challenge, with subquests and secret objectives. You can play methodically trying to do every possible type of mischief or just run around making noise.

Children of Morta is a great dungeon crawler with co-op mode and good story.

If you guys are into puzzles, Keep Talking and Nobody Explodes is just great. You have to talk a lot and describe stuff, so it is kinda... educational? But fun.

https://store.steampowered.com/app/557040/99Vidas/
https://store.steampowered.com/app/238630/Fist_Puncher/
https://store.steampowered.com/app/369890/Riddled_Corpses/
https://store.steampowered.com/app/207930/Sacred_Citadel/
https://store.steampowered.com/app/732810/Slipstream/
https://store.steampowered.com/app/341550/Super_Cyborg/
https://store.steampowered.com/app/620/Portal_2/

https://store.steampowered.com/app/1054510/Survivalist_Invisible_Strain/
https://store.steampowered.com/app/228280/Baldurs_Gate_Enhanced_Edition/
https://store.steampowered.com/app/257350/Baldurs_Gate_II_Enhanced_Edition/
https://store.steampowered.com/app/104900/ORION_Prelude/
https://store.steampowered.com/app/55230/Saints_Row_The_Third/

https://www.steamgifts.com/discussion/QgOG2/what-are-your-hidden-gems-co-op-local-or-not-steam-games
https://www.steamgifts.com/discussion/mM3i1/does-anyone-know-a-co-op-steam-games

https://store.steampowered.com/app/448510/Overcooked/
https://store.steampowered.com/app/728880/Overcooked_2/
https://store.steampowered.com/app/996770/Moving_Out/
https://store.steampowered.com/app/327030/Worms_WMD/
https://store.steampowered.com/app/477160/Human_Fall_Flat/
https://store.steampowered.com/app/204360/Castle_Crashers/
https://store.steampowered.com/app/238460/BattleBlock_Theater/
https://store.steampowered.com/app/275390/Guacamelee_Super_Turbo_Championship_Edition/
https://store.steampowered.com/app/534550/Guacamelee_2/

https://store.steampowered.com/app/225080/Brothers__A_Tale_of_Two_Sons/

Broforce
Any of the Trine games
Overcooked
Any Worms game

If your son is in a younger age group, he might like Minecraft Dungeons.
If he's a little older, For The King might be a good choice. It's a rouge-like game based on table-top rpgs, which means there's some difficulty, but maybe you two will enjoy the challenge

Here's my comment about remote play together games, but they are good for couch coop too: https://www.steamgifts.com/discussion/wWgnU/games-to-play-in-couple#6BhOyGm

Ibb & Obb

Metal Slug (any) - These are really fun 2P games.
Shank - I remember it having a two player mode.
Most sports games.

Anything else I can think of has already been mentioned.

You would be looking for games with 'local co-op' tags in Steam
-Racing games (F1 Race stars, Sonic. Horizon Chase Turbo, Hotshot Racing, Dirt Showdown)
-Shoot-em ups (Metal Slug Series, Assault Android Cactus, Mercenary kings, Rad Rodgers)
-Adventure (Never alone, Nine Parchments, LEGO City Undercover, LEGO Batman, Cat Quest II)
If I remember other kid friendly games I'll add them...cheers.

To add to the other suggestions here, maybe this https://store.steampowered.com/app/1016920/Unrailed/

And this? https://store.steampowered.com/app/1085510/Garfield_Kart__Furious_Racing/

Battleblock theater, It takes two, these two are mostly platformers. Maybe Cuphead if you would like something more challenging.